Inner-Product Matchmaking Encryption: Bilateral Access Control and Beyond Equality

We present an inner-product matchmaking encryption (IP-ME) scheme achieving weak privacy and authenticity in prime-order groups under symmetric external Diffie-Hellman (SXDH) assumption in the standard model. We further present an IP-ME with Monotone Span Program Authenticity (IP-ME with MSP Auth) scheme, where the chosen sender policy is upgraded to MSP, and the scheme also achieves weak privacy and authenticity in prime-order groups under SXDH assumption in the standard model. Both of the schemes have more expressive functionalities than identity-based matchmaking encryption (IB-ME) scheme, and are simpler than Ateniese et al.'s modular ME scheme (Crypto' 19). But our schemes only achieve a very limited flavor of security, which is reflected in the privacy.